@article {2001, title = {Lax representation and Poisson geometry of the Kowalevski top}, journal = {J. Phys. A 34 (2001) 2077-2085}, number = {SISSA;70/2000/FM}, year = {2001}, publisher = {IOP Publishing}, abstract = {We discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.}, doi = {10.1088/0305-4470/34/11/301}, url = {http://hdl.handle.net/1963/3244}, author = {Gregorio Falqui} }